Solve simultaneous linear equations: (i) 9 – (x – 4) = y + 7

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Solve simultaneous linear equations:

(i) 9 – (x – 4) = y + 7
2 (x + y) = 4 – 3y
(ii) 2x + (x – y)/ 6 = 2
x – (2x + y)/3 = 1.

Solution:

(i) 9 – (x – 4) = y + 7
2 (x + y) = 4 – 3y
We can write it as
9 – (x – 4) = y + 7
9 – x + 4 = y + 7
By further calculation
13 – x = y + 7
– x – y = 7 – 13 = – 6
x + y = 6 ….. (1)
2 (x + y) = 4 – 3y
2x + 2y = 4 – 3y
By further calculation
2x + 2y + 3y = 4
So we get
2x + 5y = 4 ….. (2)
Now multiply equation (1) by 5 and (2) by 1
5x + 5y = 30
2x + 5y = 4
By subtracting both the equations
3x = 26
So we get
x = 26/3
Substitute the value of x in (1)
26/3 + y = 6
We can write it as
y = 6 – 26/3
Taking LCM
y = (18 – 26)/3
So we get
y = – 8/3
Therefore, x = 26/3 and y = – 8/3.
(ii) 2x + (x – y)/ 6 = 2
x – (2x + y)/3 = 1
2x + (x – y)/ 6 = 2
Multiply by 6
12x + x – y = 12
By further calculation
13x – y = 12 …… (2)
x – (2x + y)/3 = 1
Multiply by 3
3x – 2x – y = 3
By further calculation
x – y = 3 …… (2)
So we get
x = 3 + y ….. (3)
Substitute the value of x in (1)
13 (3 + y) – y = 12
By further calculation
39 + 13y – y = 12
So we get
12y = 12 – 39 = – 27
By division
y = – 27/12 = – 9/4
Substitute the value of y in (3)
x = 3 + y
x = 3 + (-9)/4
By further calculation
x = 3 – 9/4
Taking LCM
x = (12 – 9)/ 4
x = ¾
Therefore, x = ¾ and y = – 9/4.

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